In Britain, stoats are part of the rhythm of nature. They prey on rabbits and rats; they are preyed on by foxes and eagles. In New Zealand, whose only land mammals were two species of bats until Europeans arrived, stoats are the single biggest threat to the unique and increasingly threatened native birdlife.

A world leader in conservation, New Zealand has saved some of its rarest birds from extinction by ridding off-shore islands of predators. Stoats, which can swim, were thought to have a maximum range of 1.5 kilometres (less than a mile). Recently, though, the sleek, furry killers have turned up on an island more than five kilometres from the mainland, raising questions about the safety of offshore sanctuaries.

Many of New Zealand's birds live and nest on the forest floor. Some, such as kakapo, weka and kiwi, are flightless. When they feel under threat, they freeze, making them easy prey for animals such as rats, cats and ferrets. Stoats – introduced in 1884 to combat a rabbit plague – are particularly formidable predators. They can tackle animals 10 times their body weight; they hunt by day as well as at night; they can travel vast distances, climb trees, and survive in almost any habitat. They are also prolific breeders, and they kill far more than they need to satisfy their hunger.

"When stoats get into a seabird colony or chicken hutch, they kill everything," says Andrew Veale, an expert on stoat genetics at Auckland University. He cites credible reports of a moorhen being attacked by a stoat and taking off into the air, with the stoat still attached. Dr Veale says: "They are phenomenal killers, with an immense bite strength."

More than 80 of New Zealand's offshore islands are pest-free sanctuaries where all mammals have been removed through trapping, shooting, and dropping poison from helicopters. Last year, a stoat was found on Rangitoto Island, more than three kilometres off Auckland. The island had been declared predator-free only a year earlier, following a NZ$3m (£1.6m) eradication programme. By analysing the stoat's DNA, Dr Veale established that it was from the mainland. This year, three stoats have been trapped on Kapiti island, a wildlife reserve 5.2 kilometres off Wellington. Dr Veale believes a female swam over and gave birth.

The destructive potential of stoats is well established. A single male killed 93 petrels on Motuotau island, in the Bay of Plenty, in four weeks. There have been instances of one or two stoats arriving on islands and wiping out entire populations. Philip Bell, a biosecurity officer with the Department of Conservation (DOC), said that if stoats could swim more than five kilometres, "there would be implications for the majority of islands around New Zealand". He added: "A couple of stoats can create a breeding colony and wipe everything out. Stoats are arguably the biggest threat to our native bird species."

They are also expensive. DOC has already spent more than NZ$200,000 trapping the three stoats on Kapiti. It will have to monitor hundreds of traps and tracking tunnels on the island for at least two years, as well as using dogs trained to detect stoats. No one is sure what prompts stoats to swim, although they appear to be in search of food. Dr Veale speculates that they take to the water after spotting land on the horizon. With the right tides, they could then travel considerable distances.

New Zealand's first offshore wildlife refuge was established in 1891, on Resolution Island, off the South Island's Fiordland coast. A decade later, stoats reached Resolution and killed off its kakapo population. However, more island sanctuaries followed, and kakapo were among the bird species rescued from extinction. Another bird, the Chatham Islands robin, was down to five individuals; but after being transferred to an island, the population recovered.